We present an improved implementation of the approximating filter for real-time seismic intensity calculations proposed in previous work. As earthquake early warning (EEW) systems become ever more widely used, the current method of computing a JMA (Japan Meteorological Agency) seismic intensity shows a serious problem since it introduces a time delay resulting from frequency domain filtering. In order to improve this method to permit real-time calculations suitable for EEW systems, we have proposed a real-time seismic intensity computed using an approximating filter in the time domain. For a simple computing system such as a strong-motion seismograph, it is straightforward to calculate the real-time seismic intensity because the approximating filter consists of only four first-order filters and one second-order filter. Based on testing using K-NET and KiK-net strong-motion seismographs, we have found that a strong-motion seismograph has enough computational capacity to undertake more sophisticated filtering. Here, we develop an approximating filter consisting of six second-order filters applied in the time domain for accurate real-time seismic intensity calculation. The relationship between the JMA seismic intensity and the real-time seismic intensity calculated using the improved approximating filter is examined using a large number of strong motion records. The results show that the differences between the JMA seismic intensities and the real-time seismic intensities are less than 0.1 for 99% of all records. Although the improved filter requires twice as much computation power as the previous approximating filter, it is suitable for EEW systems that require more accurate real-time calculations of seismic intensity.